We have researched studies on pseudorandom number generations, which are indispensable on simulations of random phenomena, and we have also studied their applications on computer simulations. On the generation of pseudorandom numbers based on the shift-real computation, Yaguchi succeeded an improvement of his original method, and he applied the theory of 1 dimensional dynamical systems, especially he employed the theory of Perron-Frobenius operators on his problem. Takenaka introduced a new method of generation of pseudorandom numbers, having a probability distribution with heavy tail.